Holographic non-perturbative corrections to gauge couplings

Understand

We give a direct microscopic derivation of the F-theory background that corresponds to four D7 branes of type I' theory by taking into account the D-instanton contributions to the emission of the axio-dilaton field in the directions transverse to the D7's.

• The couplings of the axio-dilaton to the D-instanton moduli modify its classical source terms which are shown to be proportional to the elements of the D7 brane chiral ring.
• Solving the bulk field equations with the non-perturbatively corrected sources yields the full F-theory background.
• This solution represents the gravitational dual of the four-dimensional theory living on a probe D3 brane of type I', namely of the N=2, Sp(1) SYM theory with Nf=4.